Per a different question, we've clarified that there is no way to to make "InActive" contacts, stop appearing in a search.
I lieu of that, this question is different but on the same topic.
Is there a way to make "Inactive" contacts unselectable in a Search? Via a validation rule, workflow, or process builder, etc.
This is in regards to Case>New>Contact Name>Look up:
I'm Making Progress!
I added a filter on the Contact Search Layout: